Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T17:14:12.172Z Has data issue: false hasContentIssue false
  • English
  • Français

Using R to Build and Assess Network Models inBiology

Published online by Cambridge University Press:  05 October 2011

G. Hartvigsen
G. Hartvigsen*
Affiliation:
Department of Biology, SUNY Geneseo, Geneseo, NY 14454 USA
*
⋆ Corresponding author. E-mail: [email protected]
Get access

Abstract

In this paper we build and analyze networks using the statistical and programmingenvironment R and the igraph package. We investigate random, small-world, and scale-freenetworks and test a standard problem of connectivity on a random graph. We then develop amethod to study how vaccination can alter the structure of a disease transmission network.We also discuss a variety of other uses for networks in biology.

Keywords

networksgraph theoryRigraphmodeling disease dynamics
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 6: Biomathematics Education , 2011 , pp. 61 - 75
Copyright
© EDP Sciences, 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Albert, R., Barabási, A.-L.. Statistical mechanics of complex networks. Reviews of Modern Physics, 74 (2002), 47–97. CrossRefGoogle Scholar
G. Chartrand. Introductory graph theory. Dover Publications, 1985.
M. Crawley. The R book. John Wiley & Sons, 2007.
P. Dalgaard. Introductory Statistics with R, 2/e. Springer, 2008.
Erdös, P., Rényi, A.. On Random Graphs. I. Publicationes Mathematicae, 6 (1959), 290-297. Google Scholar
Euler, L.. Solutio problematis ad geometriam situs pertinentis. Commentarii academiae scientiarum Petropolitanae, 8 (1741), 128-140. Google Scholar
Hartvigsen, G., Dresch, J.M., Zielinski, A.L., Macula, A.J., Leary, C.C.. Network structure and vaccination strategy and effort interact to affect the dynamics of influenza epidemics. Journal of Theoretical Biology, 246, Vol. 2, (2007), 205–213. CrossRefGoogle Scholar
Kermack, W.O., McKendrick, A.G.. A Contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A, 115 (1927), 700–721. CrossRefGoogle Scholar
M.E. Newman, A.-L. Barabási, D.J. Watts. The Structure and Dynamics of Networks. Princeton University Press, 2006.
M.E. Newman. Networks: an Introduction. Oxford University Press, 2010.
R Development Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing (2010), Vienna, Austria. URL http://www.R-project.org/.
Solomonoff, R., Rapoport, A.. Connectivity of random nets. Bulletin of Mathematical Biophysics, 13 (1951), 107. CrossRefGoogle Scholar
Watts, D.J., Strogatz, S.H.. Collective dynamics of "small-world" networks. Nature, 393 (1998), 440–442. CrossRefGoogle ScholarPubMed
A.F. Zuur, E.N. Ieno, E.H.W.G. Meesters. A Beginner’s Guide to R, Springer, 2009.